Arakelov geometry of toric bundles: Okounkov bodies and BKK

Fuente: arXiv
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Main Author: Hultberg, Nuno
Format: Preprint
Published: 2024
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author Hultberg, Nuno
author_facet Hultberg, Nuno
contents This article introduces the study of toric bundles and the morphisms between them from the perspective of adelic fibre bundles, as introduced by Chambert-Loir and Tschinkel. We study the Okounkov bodies and Boucksom-Chen transforms of suitable adelic line bundles on toric bundles. Finally, we prove an arithmetic analogue of a formula for intersection numbers due to Hofscheier, Khovanskii and Monin. We apply this to the study of compactifications of semiabelian varieties, whose height and successive minima we compute. This extends computations of Chambert-Loir to arbitrary toric compactifications.
format Preprint
id arxiv_https___arxiv_org_abs_2412_04169
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Arakelov geometry of toric bundles: Okounkov bodies and BKK
Hultberg, Nuno
Number Theory
Algebraic Geometry
14G40 (Primary) 14M25, 52B20 (Secondary)
This article introduces the study of toric bundles and the morphisms between them from the perspective of adelic fibre bundles, as introduced by Chambert-Loir and Tschinkel. We study the Okounkov bodies and Boucksom-Chen transforms of suitable adelic line bundles on toric bundles. Finally, we prove an arithmetic analogue of a formula for intersection numbers due to Hofscheier, Khovanskii and Monin. We apply this to the study of compactifications of semiabelian varieties, whose height and successive minima we compute. This extends computations of Chambert-Loir to arbitrary toric compactifications.
title Arakelov geometry of toric bundles: Okounkov bodies and BKK
topic Number Theory
Algebraic Geometry
14G40 (Primary) 14M25, 52B20 (Secondary)
url https://arxiv.org/abs/2412.04169